Papers by masoud namavari
Definition In everyday speech, the word " moment " refers to a short amount of time. In physics a... more Definition In everyday speech, the word " moment " refers to a short amount of time. In physics and engineering mechanics, moment is the product of a quantity and the distance from that quantity to a given point or axis. For example, in Statics, a force acting on a wrench handle produces a torque, or moment, about the axis of a bolt: M = P ! L. This is the moment of a force. We can also describe moments of areas. Consider a beam with a rectangular cross-section. The horizontal neutral axis of this beam is the x-x axis in the drawing. Take a small area " a " within the cross-section at a distance " y " from the x-x neutral axis of the beam. The first moment of this area is a ! y. The second moment of this area is I x = a ! y () ! y = ay 2. In Strength of Materials, " second moment of area " is usually abbreviated " moment of inertia ". If we divide the total area into many little areas, then the moment of inertia of the entire cross-section is the sum of the moments of inertia of all of the little areas. We can calculate the moment of inertia about the vertical y-y neutral axis: I y = a ! x () ! x = ax 2. The " x " and " y " in I x and I y refer to the neutral axis. This beam has a depth of 16 cm and a width of 5 cm. We can divide the beam into 8 equal segments 2 cm deep, 5 cm wide, so that each segment has an area a = 2 cm ! 5 cm = 10 cm 2. The centroid of segment #1 is 7 cm from the x-x axis y 1 = 7 cm () ; the centroid of segment #2 is 5 cm from the x-x axis y 2 = 5 cm () ; and so on. We can estimate the moment of inertia for the entire area as the sum of the moments of inertia of the segments, written as I x = a i y i 2 1 n ! where n = the total number of segments, and i = the number of each segment (from 1 to n), or:
Uploads
Papers by masoud namavari